Understand that cross-chain atomic swaps is for asset transfer between different cryptos.

In a world where there are different enterprise blockchains, cross-chain atomic swaps as a concept/foundation for integration between enterprise blockchain solutions (quorum, hyperledger, R3 corda) is the way forward.

As part of Stage 1, they have successfully implemented an atomic swap of ERC-223 tokens across two Ethereum chains. They plan to extend this to other Turing complete Blockchain platforms as part of Stage 2. See their blog post on Medium here: